Someone needs to stop this.
The amount of nonsense by Sir Bishop is reaching epic heights
The astronomical refraction is about 1 minute of arc when the object observed is in a heigh far from the horizon, for example, the zenit.
When the object observed is near the horizon, the refraction can come up to 30 minutes of arc (0.5º). This is the "optimal" situation, since there are many factors than can make the refraction to change, such as pollution, humidity, and others. In a normal situation, you can estimate around 40 or 50 minutes of arc, and in worst conditions, you can expect up to 60 or 70 minutes of arc
In the video you show us, the moon seems pretty close to the horizon, the pollution is quite high, so it is perfectly possible that the moon has already been set minutes ago, so those 0.5 degrees that you think are nothing, are in fact a noticeable amount.
And if you want to know more about this:
http://mintaka.sdsu.edu/GF/explain/atmos_refr/terrestrial.html